An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

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186. Required the nature of the curve which shall cut
all curves of a given species, so that the tangents at the points
of intersection may pass through the same given point.
187. Apply the result of the last example when the
curves of given species are a series of parabolas defined by
the equation y2=atx.
188. Required the curve when the curves of given species are a series of ellipses, having one of their principal axes
invariable.
189. Find the nature of the curve when the curves of
given species are a series of ellipses, having their principal
axes in a given ratio.
190. Determine the nature of the curve when the curves
of given species are cissoids of Diodes, having their axes coincident in direction.
191. Find the nature of a curve which shall cut all curves
of a given species, so that the tangents at the points of intersection may be of an invariable length: and apply the result
when the curves proposed are a series of parabolas.
192. Determine the nature of the curve cutting all curves
of a given species, so that the tangents at the points of intersection may touch a given circle.
193. Determine the nature of the curve which shall bound
a series of circles, whose respective radii are the successive ordinates of a common parabola.
194. Find the nature of the curve which shall touch all
parabolas whose areas are equal, and — whike —pats —hrough~-a
givexl -.pntpo-id have their extreme ordinates coincident in
direction.
195. If the intersection of two straight lines, which contain a given angle, be upon a line of any kind given in position,
and one of them pass through a given point, required the
nature of the curve to which the other is a tangent.